Surface energy released upon drop coalescence is known to power the self-propelled jumping of liquid droplets on superhydrophobic solid surfaces, and the jumping droplets can additionally carry colloidal payloads toward self-cleaning. Here, we show that drop coalescence on a spherical particle leads to self-propelled launching of the particle from virtually any solid surface. The main prerequisite is an intermediate wettability of the particle, such that the momentum from the capillary-inertial drop coalescence process can be transferred to the particle. By momentum conservation, the launching velocity of the particle-drop complex is proportional to the capillary-inertial velocity based on the drop radius and to the fraction of the liquid mass in the total mass. The capillary-inertial catapult is not only an alternative mechanism for removing colloidal contaminants, but also a useful model system for studying ballistospore launching.